We present a six-dimensional potential energy surface for the H2-H2 dimer based on ab initio electronic structure calculations. The surface is intended to describe accurately the bound and quasibound states of the dimers H2-H2, D2-D2, and H2-D2 that correlate with H2 or D2 monomers in the rovibrational levels (v, j) = (0, 0), (0, 2), (1, 0), and (1, 2). We use four experimentally measured transition energies for these dimers to make two empirical adjustments to the ab initio surface; the

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... d surface gives computed transition energies for 56 experimentally observed transitions that agree with experiment to within 0.036 cm^-1. For 29 of the 56 transitions, the agreement between the computed and measured transition energies is within the quoted experimental uncertainty. We use our potential energy surface to predict the energies of another 34 not-yet-observed infrared and Raman transitions for the three dimers.